The connection between Arrow theorem and Sperner lemma

2022/12/23 by Nikita Miku, Miku, Nikita
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Economics and business #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Equations Stability Results #Matrix Theory and Algorithms #Theoretical Economics (econ.TH)

paper · pdf · doi:10.48550/arxiv.2212.12251

openalex publication_date 2022/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well known that Sperner lemma is equivalent to Brouwer fixed-point theorem. Tanaka [12] proved that Brouwer theorem is equivalent to Arrow theorem, hence Arrow theorem is equivalent to Sperner lemma. In this paper we will prove this result directly. Moreover, we describe a number of other statements equivalent to Arrow theorem.

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